Question

stefan knows that a lighthouse that is 24 feet tall casts a shadow that is 45 feet long. he wants to calculate the height of a nearby climbing structure. if its shadow is 30 feet long, how tall is the climbing structure? write your answer as a whole number or a decimal. do not round.
feet

Explanation:

Step1: Set up proportion

Let \( h \) be the height of the climbing structure. The ratio of height to shadow length should be equal for both the lighthouse and the climbing structure. So, \(\frac{24}{45}=\frac{h}{30}\).

Step2: Solve for \( h \)

Cross - multiply: \( 45h = 24\times30 \).
First, calculate \( 24\times30 = 720 \). Then, \( h=\frac{720}{45} \).
Simplify \(\frac{720}{45}\): Divide numerator and denominator by 15, we get \(\frac{48}{3}=16\).

Answer:

16